Mean Entropy of States in Quantum-Statistical Mechanics

Abstract

The equilibrium states for an infinite system of quantum mechanics may be represented by states over suitably chosen C* algebras. We consider the problem of associating an entropy with these states and finding its properties, such as positivity, subadditivity, etc. For the states of a quantum-spin system, a mean entropy is defined and it is shown that this entropy is affine and upper semicontinuous.